prove that the quadrilateral formed by bisectors of angles of any quadrilateral is a cyclic quadrilateral.
Share
prove that the quadrilateral formed by bisectors of angles of any quadrilateral is a cyclic quadrilateral.
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
ABCD is a cyclic quadrilateral
∠A+∠C=180° and ∠B+∠D = 180°
(∠A+∠C)/2=90°and(∠B+∠D)/2= 90°
w,x,y,z are angles of the inner quadrilateral
x + z = 90°
y + w = 90°
In ΔAGD and ΔBEC,
x + y + ∠AGD = 180°
z + w + ∠BEC = 180°
∠AGD = 180° – (x+y)
∠BEC = 180° – (z+w)
∠AGD+∠BEC=360°-(x+y+z+w)
= 360° – (90+90) = 360° – 180° = 180°
∠AGD+∠BEC = 180°
∠FGH+∠HEF = 180°
The sum of a pair of opposite angles of a quadrilateral EFGH is 180°.
Hence EFGH is cyclic
Hence Proved
Hope it is helpful for u....
If yes then plz mark it as brainliest...
Plz it's a request to u....